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932                           Appendix III.

three Lancashire boilers of 7 ft, 7'.. 6", and 8 ft. diameter
respectively, on the previous premises, we must first find G the
grate surface. Taking all grate width at 6 ft., we have :

For 7 ft. boiler, grates about 6 ft. long, and area = 36 sq. ft.

p.  ..                      _

o                  —       v_J                       —     C7 vji     —     ii«_)c-»

Similarly for the j'..6" boiler, grates about 6'..6" long'
and area  =  39 sq. ft

.-.    I H. P.   =  8G  -  8x39  =  312

And  for the 8 ft.  boiler,  grates  about 7 ft. long,  and
area  =  42 sq. ft.

.-.    LH.P. = 8x42  =  336

For other boilers the evaporation would depend upon the
efficiency as compared with the above; and perhaps the steam
used by the engine might be raised to 30 Ibs. wt. per I. H, P. hour.

Si; i jj                             jP. 674.  Acceleration of Engine Piston : Klein's con-

4'  '.                        struction.

\ 4    ' ,*

ft*1   „                                  When   drawing  an   acceleration curve to  a  given  velocity

p,j 1                            curve two cases present  themselves, one where  the  base line

tlj   /                            represents time, and the other where it shews distance.    The

if   A                            construction for the former, p. 860, is easily and correctly met

I!   ;*<                            by graphic differentiation,    For a distance base, Proell's method,

i|    i\                            pp. 492 and 863, is very convenient for general cases, but when

*"'•   „                            adopted for the harmonic motion of an engine piston, as at

f                            p. 674, it does not give absolute results at the dead points.   We

shall, therefore, here describe the construction due to Prof. Klein
( !'j                            of America, which, though more cumbersome, and only applicable

\l                            to the crank and connecting-rod, gives certain aad accurate

1 '#                            values at all points of the stroke.

Referring to Fig. 886, let AB be the crank and BC the con-
necting-rod. On BC as diameter describe a circle. Producing
c B to i>, describe a second circle having B as centre and B D
as radius, and cutting the frst circle in E and P. Then, EF
will cross AC in G, and GA will be the acceleration of c, which